This talk concerns a nonlinear partial differential system in a 3-dimensional domain involving the operator curl^2, which is a simplified model used to examine nucleation of instability of the Meissner state of a superconductor as the applied magnetic field reaches the superheating field. We derive a priori C^(2+alpha) estimates for a weak solution H, the curl of the magnetic potential, and determine the location of the maximal points of |curl H| which correspond to the nucleation of instability of the Meissner state. We show that, if the penetration length is small, the solution exhibits a boundary layer. If the applied magnetic field is homogeneous, |curl H| is maximal around the points on the boundary where the applied field is tangential to the surface. Note: This talk is held on Monday, May 5th, 3-4pm, in Carslaw 273!